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# Title: Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio (shelfmark Leibn. Marg. 84:2)
# Folio 130, page id 824573315:0342
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130
Arithmetica Infinitorum.
PrOP. 165.
quae minus acthuc ridecur incelligibilis quam abi ponicur radi-
es parcium pauciorum, Dut2 6.
Acg; eodem modo quo plures supponuntur radii partes co
incriestior necesse cstur hiar rationis explicario; quae quidem
Fere omnium radicum repecirionem postulet, cum paucae ad-
modum, raro quidem, _ non nili Forcnico qua(I, OCCu. ruNE, qua
vel racionales line vel quidem invicem commenturabiles. LF
Propcerca si Cupponacur Radius parcium intinicarum, racio
Proreniens eciam minus achuc vidcacur explicabilis.
Idem concingeret, li, JuXta CenOrEM PTOP. 135. DONaTuIE
circuli Diamecer parcium 12. Iea enim elfene Sinus recti corre
spondences in Semicieculo. V: Ox T2 - O: +V: 2Z T2 - 1:
4. V: 2X224: F V: 3C229: +~: 4212 - 16: +V: 5X 12
 25. + V: 6X12 n 36: + V: 7 X+2 no 43: + V: 8 XI2 in 64: + V3
OXF2 nn 8F: + V: 1OX F2 = 100: +V: ELX 12 = 121. FV: 1DX 12
on 144. HdC cR V: 0 - O: F V: 12 = L: + V: 24 = 4: +V: 36
d: tr: 48  16: +V: 60 nn 25: + V. 72 = 36: tV: 84 n 49:
N: 96 - 64: F V: 108 n 8T: FV: 120 - 100: + V: 132 - 1215
V: 144 = 144. HoC eA N0+ ~ TTFV2O+ V27+ 1324  35
rN36 + V35 + 132+V27+V20+ V11 +V0. Ve provice
ealdem radices bis oolicas, 2V0 +2V Tr2 2V20 + 2V27 +2N32
42V35) f ~36 Vel, reducendo irracionalicacem ad minimos
terminoe, o+2V1I ++ V5 +6V3+8V2+2V35+6. Racio igi-
cur quam habet hoc 20gregacum ad cocidem radices maximae
aequales, puta ad 13V36 vel 1376, hoc cA, ad78, non exrli-
cacius eHferri porerit quam 2V 12 14V 5+6 Y3+ a V +2Y3576.
vet
N71 + 2N5+ ~ 2+. N2 +. 25 +.2
ACq; ea est rario
quam habet rogresacum istorum sinuum rectorum in Semi
circulo, od cocidem rectas radio equales e parallelas in Paral
leloerammo huic Cemicirculo circumseripeo Siaucem InuS
moximus V36=6 lueponacur bis poni (peo vrroqi Ccilicet
quadsante (emel) acqi capropter pro 13 xqualibus, POnantuE
24; (DATa, DeN 1316- = 78 DOnaCUCT4n 6-84;) eadem erit
hiac racio cum ea quam lupra proveuire diximus polito radio
Parcium CCX.
Paricer, si Diamecee ponatur partium 20; tnus recti in Se.
MmiLIFCULOCTINE V: OK_O  O: LY: R X2O= 1: +. Y: 2720- 4: